The screen is 16-color greyscale and refreshes slowly (for apps); I'm having trouble thinking of what app would be better on a kindle than an iPhone. The screen size is the only real advantage I see. I'd love to proven wrong, but I just don't see the Kindle store taking off.
I think we could also see apps that use the kindle as a tool for producing content, not just consuming it. Writing blog posts, kindle twitter apps, etc. The keyboard leaves something to be desired, but I could still see this type of thing being popular.
Basically, the successful apps won't be competing with what you see on the iphone, they'll be unique to the device.
I wrote a four-line HN comment from my Kindle the other day, because my cell phone ran out of batteries. It was excruciating. T H E L E tters appeared one at a time with enough of a pause in between them that even with the non-standard layout of the keyboard I had queued up two sentences and then had to wait for literally 45 seconds while my Kindle caught up to me.
The thought of writing a substantive blog post on the Kindle scares me.
The only things unique about Kindle apps will be the slightly larger screen, lack of animation, lack of color, and lack of unlimited data transfer.